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关于幂和公式的一般性质 总被引:23,自引:0,他引:23
一、前言 当n与k都是正整数时,我们简称sum from m=1 to n ()m~k为“幂和”,并以S_k(n)记之。从古希腊的阿基米德开始,这个问题就吸引着很多数学家的兴趣。十七世纪以前的数学家们仅仅求出了二次和三次幂的求和公式。而雅各·伯努利在《猜度术》中,一举得到了任意次幂的求和公式如下: 相似文献
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论文《由两道概率论习题引发的讨论》(数学通报,2004.6以下简称为文),是从两道概率论习题引发出各自的推广形式,但文中推广形式的结论表达式①,②以及证明存在不妥,在此共同商榷. 相似文献
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将常见的离散型随机变量的分布用一个与伯努利试验有关的题目加以整合,揭示了怎样由伯努利试验构造离散型随机变量的分布.并举出了基于伯努利试验的离散型随机变量的分布在解决相关问题中的例子.实例表明用伯努利试验研究离散型随机变量的分布及相关问题.会起到事半功倍的效果. 相似文献
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张尧庭主编的《概率统计》教材.是一部探索性色彩浓厚的教科书.该教本弥合了概率论与散理统计之间的人为鸿沟.强调分析过程,注重抽象建模,借助现代化的视听手段,创新了概率统计教科书的传统规范,顺应了当代教育改革的大趋势.张尧庭在授课艺术与研究方略方面,有乃师许宝騄的风范.由于针对性较差等原因,《概率统计》教本远未达到预期的效果. 相似文献
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n元Euler数和多项式与n元Bernoulli数和多项式 总被引:1,自引:0,他引:1
本文给出了n元Euler数,n元Bernoulli数,n元Euler多项式,n元Bernoulli多项式的定义,导出了它们的母函数,得到了n元Euler数与Euler数n元Bernoulli数与Bernoulli数,n元Euler多项式与Bernoulli多项式的关系式。 相似文献
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Dj. S. Djukic T. M. Atanackovic 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1976,2(6):677-681
It is shown that the classical Bernoulli's brachistochrone problem and the brachistochrone problem in a central force field may be solved by the maximum principle of Pontryagin. According to the optimum control theory these problems are singular. 相似文献
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In a recent paper Longuet-Higgins (1978) discovered some newrelations between Stokes' coefficients in the theory of periodicgravity waves. These were shown to give rise to a set of integralrelations. In this paper we show that this set is complete inthe sense that it is equivalent to Bernoulli's equation. Wealso show that a suitably redefined set exists in the theoryof the solitary wave. 相似文献
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高阶多元Euler多项式和高阶多元Bernoulli多项式 总被引:1,自引:1,他引:0
本文给出了高阶多元Euler数和多项式与高阶多元Bernouli数和多项式的定义,讨论了它们的一些重要性质,得到了高阶多元Euler多项式(数)和高阶多元Bernouli多项式(数)的关系式· 相似文献
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ANDREI KHRENNIKOV 《应用数学学报(英文版)》1996,12(1):78-92
ANDREIKHRENNIKOV(DepartmentofHighMathematics,MoscowInstituteofElectronicEngineering,103498,Moscow,K-498,Russian)(Thisworkissu... 相似文献
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通过引入带参数的指数积分并利用Bernoulli不等式以及改进了的Hlder不等式,对Hardy-Hilbert积分不等式作了有意义改进.特别,当p=2时,得到了经典的Hilbert积分不等式的一个很强的结果. 相似文献
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We review several of de Finetti’s fundamental contributions where these have played and continue to play an important role in the development of imprecise probability research. Also, we discuss de Finetti’s few, but mostly critical remarks about the prospects for a theory of imprecise probabilities, given the limited development of imprecise probability theory as that was known to him. 相似文献
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Dj. S. Djukic T. M. Atanackovic 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1976,27(5):677-681
Summary It is shown that the classical Bernoulli's brachistochrone problem and the brachistochrone problem in a central force field may be solved by the maximum principle of Pontryagin. According to the optimum control theory these problems are singular.
Zusammenfassung In der Arbeit ist gezeigt, daß das klassische Bernoullische brachistochrone Problem und Brachistochronen im zentralen Schwerefeld durch das Pontryagin Maximum Prinzip gelöst werden können. Gemäss Theorie der optimalen Regelung sind diese Probleme singulär.相似文献
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B. Maga 《Acta Mathematica Hungarica》2018,156(1):145-171
In the previous decades, the theory of first passage percolation became a highly important area of probability theory. In this work, we will observe what can be said about the corresponding structure if we forget about the probability measure defined on the product space of edges and simply consider topology in the terms of residuality. We focus on interesting questions arising in the probabilistic setup that make sense in this setting, too. We will see that certain classical almost sure events, as the existence of geodesics have residual counterparts, while the notion of the limit shape or time constants gets as chaotic as possible. 相似文献